The present invention relates to apparatus and methods for coding and for decoding. In particular, it relates to methods and apparatus for coding and for decoding that apply an implementation of at least an n-state addition over an alternate finite field GF(n) and at least one n-state inverter defined by a multiplication over the alternate finite field GF(n) or an implementation of a truth table defined by said addition and inverter, with n>2, with n>3 or with n>4.
Finite fields GF(n), including classical extension fields are known. Presently, certain type of coders apply additions and multiplications over a classical finite field GF(n). This makes certain elements of an encoder and/or decoder relatively predictable. It would make a coded signal of n-state symbols with n>2, n>3 or n>4, including certain check symbols generated as part of a code word less predictable if novel functions with attractive properties as defined in an alternate and currently unknown finite field would be used.
Accordingly, novel and improved methods and apparatus for encoding and decoding n-state symbols with functions defined over an alternate finite field are required.